Polytope of Type {18,46}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {18,46}*1656
Also Known As : {18,46|2}. if this polytope has another name.
Group : SmallGroup(1656,40)
Rank : 3
Schlafli Type : {18,46}
Number of vertices, edges, etc : 18, 414, 46
Order of s₀s₁s₂ : 414
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {6,46}*552
   9-fold quotients : {2,46}*184
   18-fold quotients : {2,23}*92
   23-fold quotients : {18,2}*72
   46-fold quotients : {9,2}*36
   69-fold quotients : {6,2}*24
   138-fold quotients : {3,2}*12
   207-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2,  3)(  5,  6)(  8,  9)( 11, 12)( 14, 15)( 17, 18)( 20, 21)( 23, 24)
( 26, 27)( 29, 30)( 32, 33)( 35, 36)( 38, 39)( 41, 42)( 44, 45)( 47, 48)
( 50, 51)( 53, 54)( 56, 57)( 59, 60)( 62, 63)( 65, 66)( 68, 69)( 70,140)
( 71,139)( 72,141)( 73,143)( 74,142)( 75,144)( 76,146)( 77,145)( 78,147)
( 79,149)( 80,148)( 81,150)( 82,152)( 83,151)( 84,153)( 85,155)( 86,154)
( 87,156)( 88,158)( 89,157)( 90,159)( 91,161)( 92,160)( 93,162)( 94,164)
( 95,163)( 96,165)( 97,167)( 98,166)( 99,168)(100,170)(101,169)(102,171)
(103,173)(104,172)(105,174)(106,176)(107,175)(108,177)(109,179)(110,178)
(111,180)(112,182)(113,181)(114,183)(115,185)(116,184)(117,186)(118,188)
(119,187)(120,189)(121,191)(122,190)(123,192)(124,194)(125,193)(126,195)
(127,197)(128,196)(129,198)(130,200)(131,199)(132,201)(133,203)(134,202)
(135,204)(136,206)(137,205)(138,207)(209,210)(212,213)(215,216)(218,219)
(221,222)(224,225)(227,228)(230,231)(233,234)(236,237)(239,240)(242,243)
(245,246)(248,249)(251,252)(254,255)(257,258)(260,261)(263,264)(266,267)
(269,270)(272,273)(275,276)(277,347)(278,346)(279,348)(280,350)(281,349)
(282,351)(283,353)(284,352)(285,354)(286,356)(287,355)(288,357)(289,359)
(290,358)(291,360)(292,362)(293,361)(294,363)(295,365)(296,364)(297,366)
(298,368)(299,367)(300,369)(301,371)(302,370)(303,372)(304,374)(305,373)
(306,375)(307,377)(308,376)(309,378)(310,380)(311,379)(312,381)(313,383)
(314,382)(315,384)(316,386)(317,385)(318,387)(319,389)(320,388)(321,390)
(322,392)(323,391)(324,393)(325,395)(326,394)(327,396)(328,398)(329,397)
(330,399)(331,401)(332,400)(333,402)(334,404)(335,403)(336,405)(337,407)
(338,406)(339,408)(340,410)(341,409)(342,411)(343,413)(344,412)(345,414);;
s1 := (  1, 70)(  2, 72)(  3, 71)(  4,136)(  5,138)(  6,137)(  7,133)(  8,135)
(  9,134)( 10,130)( 11,132)( 12,131)( 13,127)( 14,129)( 15,128)( 16,124)
( 17,126)( 18,125)( 19,121)( 20,123)( 21,122)( 22,118)( 23,120)( 24,119)
( 25,115)( 26,117)( 27,116)( 28,112)( 29,114)( 30,113)( 31,109)( 32,111)
( 33,110)( 34,106)( 35,108)( 36,107)( 37,103)( 38,105)( 39,104)( 40,100)
( 41,102)( 42,101)( 43, 97)( 44, 99)( 45, 98)( 46, 94)( 47, 96)( 48, 95)
( 49, 91)( 50, 93)( 51, 92)( 52, 88)( 53, 90)( 54, 89)( 55, 85)( 56, 87)
( 57, 86)( 58, 82)( 59, 84)( 60, 83)( 61, 79)( 62, 81)( 63, 80)( 64, 76)
( 65, 78)( 66, 77)( 67, 73)( 68, 75)( 69, 74)(139,140)(142,206)(143,205)
(144,207)(145,203)(146,202)(147,204)(148,200)(149,199)(150,201)(151,197)
(152,196)(153,198)(154,194)(155,193)(156,195)(157,191)(158,190)(159,192)
(160,188)(161,187)(162,189)(163,185)(164,184)(165,186)(166,182)(167,181)
(168,183)(169,179)(170,178)(171,180)(172,176)(173,175)(174,177)(208,277)
(209,279)(210,278)(211,343)(212,345)(213,344)(214,340)(215,342)(216,341)
(217,337)(218,339)(219,338)(220,334)(221,336)(222,335)(223,331)(224,333)
(225,332)(226,328)(227,330)(228,329)(229,325)(230,327)(231,326)(232,322)
(233,324)(234,323)(235,319)(236,321)(237,320)(238,316)(239,318)(240,317)
(241,313)(242,315)(243,314)(244,310)(245,312)(246,311)(247,307)(248,309)
(249,308)(250,304)(251,306)(252,305)(253,301)(254,303)(255,302)(256,298)
(257,300)(258,299)(259,295)(260,297)(261,296)(262,292)(263,294)(264,293)
(265,289)(266,291)(267,290)(268,286)(269,288)(270,287)(271,283)(272,285)
(273,284)(274,280)(275,282)(276,281)(346,347)(349,413)(350,412)(351,414)
(352,410)(353,409)(354,411)(355,407)(356,406)(357,408)(358,404)(359,403)
(360,405)(361,401)(362,400)(363,402)(364,398)(365,397)(366,399)(367,395)
(368,394)(369,396)(370,392)(371,391)(372,393)(373,389)(374,388)(375,390)
(376,386)(377,385)(378,387)(379,383)(380,382)(381,384);;
s2 := (  1,211)(  2,212)(  3,213)(  4,208)(  5,209)(  6,210)(  7,274)(  8,275)
(  9,276)( 10,271)( 11,272)( 12,273)( 13,268)( 14,269)( 15,270)( 16,265)
( 17,266)( 18,267)( 19,262)( 20,263)( 21,264)( 22,259)( 23,260)( 24,261)
( 25,256)( 26,257)( 27,258)( 28,253)( 29,254)( 30,255)( 31,250)( 32,251)
( 33,252)( 34,247)( 35,248)( 36,249)( 37,244)( 38,245)( 39,246)( 40,241)
( 41,242)( 42,243)( 43,238)( 44,239)( 45,240)( 46,235)( 47,236)( 48,237)
( 49,232)( 50,233)( 51,234)( 52,229)( 53,230)( 54,231)( 55,226)( 56,227)
( 57,228)( 58,223)( 59,224)( 60,225)( 61,220)( 62,221)( 63,222)( 64,217)
( 65,218)( 66,219)( 67,214)( 68,215)( 69,216)( 70,280)( 71,281)( 72,282)
( 73,277)( 74,278)( 75,279)( 76,343)( 77,344)( 78,345)( 79,340)( 80,341)
( 81,342)( 82,337)( 83,338)( 84,339)( 85,334)( 86,335)( 87,336)( 88,331)
( 89,332)( 90,333)( 91,328)( 92,329)( 93,330)( 94,325)( 95,326)( 96,327)
( 97,322)( 98,323)( 99,324)(100,319)(101,320)(102,321)(103,316)(104,317)
(105,318)(106,313)(107,314)(108,315)(109,310)(110,311)(111,312)(112,307)
(113,308)(114,309)(115,304)(116,305)(117,306)(118,301)(119,302)(120,303)
(121,298)(122,299)(123,300)(124,295)(125,296)(126,297)(127,292)(128,293)
(129,294)(130,289)(131,290)(132,291)(133,286)(134,287)(135,288)(136,283)
(137,284)(138,285)(139,349)(140,350)(141,351)(142,346)(143,347)(144,348)
(145,412)(146,413)(147,414)(148,409)(149,410)(150,411)(151,406)(152,407)
(153,408)(154,403)(155,404)(156,405)(157,400)(158,401)(159,402)(160,397)
(161,398)(162,399)(163,394)(164,395)(165,396)(166,391)(167,392)(168,393)
(169,388)(170,389)(171,390)(172,385)(173,386)(174,387)(175,382)(176,383)
(177,384)(178,379)(179,380)(180,381)(181,376)(182,377)(183,378)(184,373)
(185,374)(186,375)(187,370)(188,371)(189,372)(190,367)(191,368)(192,369)
(193,364)(194,365)(195,366)(196,361)(197,362)(198,363)(199,358)(200,359)
(201,360)(202,355)(203,356)(204,357)(205,352)(206,353)(207,354);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(414)!(  2,  3)(  5,  6)(  8,  9)( 11, 12)( 14, 15)( 17, 18)( 20, 21)
( 23, 24)( 26, 27)( 29, 30)( 32, 33)( 35, 36)( 38, 39)( 41, 42)( 44, 45)
( 47, 48)( 50, 51)( 53, 54)( 56, 57)( 59, 60)( 62, 63)( 65, 66)( 68, 69)
( 70,140)( 71,139)( 72,141)( 73,143)( 74,142)( 75,144)( 76,146)( 77,145)
( 78,147)( 79,149)( 80,148)( 81,150)( 82,152)( 83,151)( 84,153)( 85,155)
( 86,154)( 87,156)( 88,158)( 89,157)( 90,159)( 91,161)( 92,160)( 93,162)
( 94,164)( 95,163)( 96,165)( 97,167)( 98,166)( 99,168)(100,170)(101,169)
(102,171)(103,173)(104,172)(105,174)(106,176)(107,175)(108,177)(109,179)
(110,178)(111,180)(112,182)(113,181)(114,183)(115,185)(116,184)(117,186)
(118,188)(119,187)(120,189)(121,191)(122,190)(123,192)(124,194)(125,193)
(126,195)(127,197)(128,196)(129,198)(130,200)(131,199)(132,201)(133,203)
(134,202)(135,204)(136,206)(137,205)(138,207)(209,210)(212,213)(215,216)
(218,219)(221,222)(224,225)(227,228)(230,231)(233,234)(236,237)(239,240)
(242,243)(245,246)(248,249)(251,252)(254,255)(257,258)(260,261)(263,264)
(266,267)(269,270)(272,273)(275,276)(277,347)(278,346)(279,348)(280,350)
(281,349)(282,351)(283,353)(284,352)(285,354)(286,356)(287,355)(288,357)
(289,359)(290,358)(291,360)(292,362)(293,361)(294,363)(295,365)(296,364)
(297,366)(298,368)(299,367)(300,369)(301,371)(302,370)(303,372)(304,374)
(305,373)(306,375)(307,377)(308,376)(309,378)(310,380)(311,379)(312,381)
(313,383)(314,382)(315,384)(316,386)(317,385)(318,387)(319,389)(320,388)
(321,390)(322,392)(323,391)(324,393)(325,395)(326,394)(327,396)(328,398)
(329,397)(330,399)(331,401)(332,400)(333,402)(334,404)(335,403)(336,405)
(337,407)(338,406)(339,408)(340,410)(341,409)(342,411)(343,413)(344,412)
(345,414);
s1 := Sym(414)!(  1, 70)(  2, 72)(  3, 71)(  4,136)(  5,138)(  6,137)(  7,133)
(  8,135)(  9,134)( 10,130)( 11,132)( 12,131)( 13,127)( 14,129)( 15,128)
( 16,124)( 17,126)( 18,125)( 19,121)( 20,123)( 21,122)( 22,118)( 23,120)
( 24,119)( 25,115)( 26,117)( 27,116)( 28,112)( 29,114)( 30,113)( 31,109)
( 32,111)( 33,110)( 34,106)( 35,108)( 36,107)( 37,103)( 38,105)( 39,104)
( 40,100)( 41,102)( 42,101)( 43, 97)( 44, 99)( 45, 98)( 46, 94)( 47, 96)
( 48, 95)( 49, 91)( 50, 93)( 51, 92)( 52, 88)( 53, 90)( 54, 89)( 55, 85)
( 56, 87)( 57, 86)( 58, 82)( 59, 84)( 60, 83)( 61, 79)( 62, 81)( 63, 80)
( 64, 76)( 65, 78)( 66, 77)( 67, 73)( 68, 75)( 69, 74)(139,140)(142,206)
(143,205)(144,207)(145,203)(146,202)(147,204)(148,200)(149,199)(150,201)
(151,197)(152,196)(153,198)(154,194)(155,193)(156,195)(157,191)(158,190)
(159,192)(160,188)(161,187)(162,189)(163,185)(164,184)(165,186)(166,182)
(167,181)(168,183)(169,179)(170,178)(171,180)(172,176)(173,175)(174,177)
(208,277)(209,279)(210,278)(211,343)(212,345)(213,344)(214,340)(215,342)
(216,341)(217,337)(218,339)(219,338)(220,334)(221,336)(222,335)(223,331)
(224,333)(225,332)(226,328)(227,330)(228,329)(229,325)(230,327)(231,326)
(232,322)(233,324)(234,323)(235,319)(236,321)(237,320)(238,316)(239,318)
(240,317)(241,313)(242,315)(243,314)(244,310)(245,312)(246,311)(247,307)
(248,309)(249,308)(250,304)(251,306)(252,305)(253,301)(254,303)(255,302)
(256,298)(257,300)(258,299)(259,295)(260,297)(261,296)(262,292)(263,294)
(264,293)(265,289)(266,291)(267,290)(268,286)(269,288)(270,287)(271,283)
(272,285)(273,284)(274,280)(275,282)(276,281)(346,347)(349,413)(350,412)
(351,414)(352,410)(353,409)(354,411)(355,407)(356,406)(357,408)(358,404)
(359,403)(360,405)(361,401)(362,400)(363,402)(364,398)(365,397)(366,399)
(367,395)(368,394)(369,396)(370,392)(371,391)(372,393)(373,389)(374,388)
(375,390)(376,386)(377,385)(378,387)(379,383)(380,382)(381,384);
s2 := Sym(414)!(  1,211)(  2,212)(  3,213)(  4,208)(  5,209)(  6,210)(  7,274)
(  8,275)(  9,276)( 10,271)( 11,272)( 12,273)( 13,268)( 14,269)( 15,270)
( 16,265)( 17,266)( 18,267)( 19,262)( 20,263)( 21,264)( 22,259)( 23,260)
( 24,261)( 25,256)( 26,257)( 27,258)( 28,253)( 29,254)( 30,255)( 31,250)
( 32,251)( 33,252)( 34,247)( 35,248)( 36,249)( 37,244)( 38,245)( 39,246)
( 40,241)( 41,242)( 42,243)( 43,238)( 44,239)( 45,240)( 46,235)( 47,236)
( 48,237)( 49,232)( 50,233)( 51,234)( 52,229)( 53,230)( 54,231)( 55,226)
( 56,227)( 57,228)( 58,223)( 59,224)( 60,225)( 61,220)( 62,221)( 63,222)
( 64,217)( 65,218)( 66,219)( 67,214)( 68,215)( 69,216)( 70,280)( 71,281)
( 72,282)( 73,277)( 74,278)( 75,279)( 76,343)( 77,344)( 78,345)( 79,340)
( 80,341)( 81,342)( 82,337)( 83,338)( 84,339)( 85,334)( 86,335)( 87,336)
( 88,331)( 89,332)( 90,333)( 91,328)( 92,329)( 93,330)( 94,325)( 95,326)
( 96,327)( 97,322)( 98,323)( 99,324)(100,319)(101,320)(102,321)(103,316)
(104,317)(105,318)(106,313)(107,314)(108,315)(109,310)(110,311)(111,312)
(112,307)(113,308)(114,309)(115,304)(116,305)(117,306)(118,301)(119,302)
(120,303)(121,298)(122,299)(123,300)(124,295)(125,296)(126,297)(127,292)
(128,293)(129,294)(130,289)(131,290)(132,291)(133,286)(134,287)(135,288)
(136,283)(137,284)(138,285)(139,349)(140,350)(141,351)(142,346)(143,347)
(144,348)(145,412)(146,413)(147,414)(148,409)(149,410)(150,411)(151,406)
(152,407)(153,408)(154,403)(155,404)(156,405)(157,400)(158,401)(159,402)
(160,397)(161,398)(162,399)(163,394)(164,395)(165,396)(166,391)(167,392)
(168,393)(169,388)(170,389)(171,390)(172,385)(173,386)(174,387)(175,382)
(176,383)(177,384)(178,379)(179,380)(180,381)(181,376)(182,377)(183,378)
(184,373)(185,374)(186,375)(187,370)(188,371)(189,372)(190,367)(191,368)
(192,369)(193,364)(194,365)(195,366)(196,361)(197,362)(198,363)(199,358)
(200,359)(201,360)(202,355)(203,356)(204,357)(205,352)(206,353)(207,354);
poly := sub<Sym(414)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

References : None.
to this polytope